| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion |
|---|---|---|---|---|
| 1 | 19 | 50 | 10 | last |
| 2 | 14 | 50 | 10 | last |
| 3 | 19 | 50 | 20 | last |
| 4 | 14 | 50 | 20 | last |
| 5 | 19 | 50 | 10 | nearest |
| 6 | 14 | 50 | 10 | nearest |
| 7 | 19 | 50 | 20 | nearest |
| 8 | 14 | 50 | 20 | nearest |
Modelling Fecal Cortisol Metabolites
Dr. Nicolas Ferry - Bavarian National Forest (?) / Daniel Schlichting - StabLab
31 Jan 2025
assess red deer stress response towards hunting activities
– on 41 individual collared red deer
– within Bavarian Forest National Park
– using FCMs
FCMs: Faecal Cortisol Metabolites - a non-invasive method to measure stress through faecal samples
collared deer: red deer wearing a GPS-collar, which provides hourly location information
Euclidean Distance: Also known as \(L^2\) Distance. Reduces to Pythagorean Theorem for two Dimensions: \[d_{x,y} = ((x_1 - y_1)^2 + (x_2 - y_2)^2)^\frac{1}{2} \\ x,y \in \mathbb{R}^2 \]
model FCM levels on spatial and temporal distance to hunting activities
Expectation: FCM levels higher when closer in time and space
Movement: contains the location and datetime of the 41 collared deer in the period Feb 2020 - Feb 2023. In total approx. 740 000 observations1
Hunting Events: contains location and date of hunting events in the National Park - in total 1270 events, 890 of them with full timestamp
FCM Stress: contains information of 809 faecal samples, including:
– the location of the sample
– the time of sampling
– the DNA-matched collared deer
– the time when the deer was at the location
Reproduction Success: observations of 16 collared deer on:
– if they were pregnant in one year
– if they were accompanied by a calf in one year
We introduce 4 Parameters:
Gut Retention Time (GRT) low: The minimum amount of hours, a Stress Event can appear before Defecation Time
Gut Retention Time (GRT) high: The maximimum amount of hours, a Stress Event can appear before Defecation Time
Distance Threshold: The maximum spatial Distance of a Deer to a given Hunting Event to be considered
Proximity Criterion: We consider either the Hunting Event closest in Space or in Time to be the most relevant
We suggest eight different Datasets for Modelling
| DataSet | GRT low | GRT high | Distance Threshold | Proximity Criterion |
|---|---|---|---|---|
| 1 | 19 | 50 | 10 | last |
| 2 | 14 | 50 | 10 | last |
| 3 | 19 | 50 | 20 | last |
| 4 | 14 | 50 | 20 | last |
| 5 | 19 | 50 | 10 | nearest |
| 6 | 14 | 50 | 10 | nearest |
| 7 | 19 | 50 | 20 | nearest |
| 8 | 14 | 50 | 20 | nearest |
\(FCM_i \sim \mathcal{N}(\mu_i, \sigma^2)\)
Identity Link: \(E(FCM_i) = \mu_i = \eta_i\)
Linear Predictor: \[ \begin{equation} \begin{gathered} \eta_i = \beta_0 + \beta_1\,Pregnant_i +\\ \beta_2\,Number\,Other\,Hunts_i + f_1(Time\,Diff_i) + \\ f_2(Distance_i) + f_3(Sample\,Delay_i) + f_4(Day\,of\,Year_i) \end{gathered} \end{equation} \]
\(FCM_i \sim \mathcal{Ga}(\nu, \frac{\nu}{\mu_i})\)
For better Interpretability we use the Log-Link: \(E(FCM_i) = \mu_i = exp(\eta_i)\)
Linear Predictor: \[ \begin{equation} \begin{gathered} \eta_i = \beta_0 + \beta_1\,Pregnant_i +\\ \beta_2\,Number\,Other\,Hunts_i + f_1(Time\,Diff_i) + \\ f_2(Distance_i) + f_3(Sample\,Delay_i) + f_4(Day\,of\,Year_i) \end{gathered} \end{equation} \]
\(FCM_{i\,j} \sim \mathcal{N}(\mu_{i\,j}, \sigma^2)\)
Identity Link: \(E(FCM_{i\,j}) = \mu_{i\,j} = \eta_{i\,j}\)
Linear Predictor: \[ \begin{equation} \begin{gathered} \eta_{i\,j} = \beta_0 + \beta_1\,Pregnant_{i\,j} +\\ \beta_2\,Number\,Other\,Hunts_{i\,j} + f_1(Time\,Diff_{i\,j}) + \\ f_2(Distance_{i\,j}) + f_3(Sample\,Delay_{i\,j}) + f_4(Day\,of\,Year_{i\,j}) \end{gathered} \end{equation} \] with: \(\gamma_j \overset{\mathrm{iid}}{\sim} \mathcal{N}(0, \sigma_{\gamma}^2)\)
\(FCM_{i\,j} \sim \mathcal{Ga}(\nu, \frac{\nu}{\mu_{i\,j}})\)
For better Interpretability we use the Log-Link: \(E(FCM_{i\,j}) = \mu_{i\,j} = exp(\eta_{i\,j})\)
Linear Predictor: \[ \begin{equation} \begin{gathered} \eta_{i\,j} = \beta_0 + \beta_1\,Pregnant_{i\,j} +\\ \beta_2\,Number\,Other\,Hunts_{i\,j} + f_1(Time\,Diff_{i\,j}) + \\ f_2(Distance_{i\,j}) + f_3(Sample\,Delay_{i\,j}) + f_4(Day\,of\,Year_{i\,j}) + \\ \gamma_j \end{gathered} \end{equation} \]
with: \(\gamma_j \overset{\mathrm{iid}}{\sim} \mathcal{N}(0, \sigma_{\gamma}^2)\)
Not enough observations after the datafusion left for robust modelling
Effect of Hunting on Red Deer